Geometry Regents Exam 0113www.jmap.org

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0113ge

1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX ?

1) XV

2) WX

3) VW

4) NP

2 In circle O shown in the diagram below, chords AB

and CD are parallel.

If mAB 104 and mCD 168, what is mBD?1) 382) 443) 884) 96

3 As shown in the diagram below, CD is a median of ABC.

Which statement is always true?

1) AD DB

2) AC AD3) ACD CDB4) BCD ACD

4 In the diagram below, under which transformation is AB C the image of ABC?

1) D2

2) rx-axis

3) r y-axis

4) (x, y) (x 2, y)

5 Line segment AB is a diameter of circle O whose center has coordinates (6, 8). What are the coordinates of point B if the coordinates of point A are (4, 2)?1) (1, 3)2) (5, 5)3) (8, 14)4) (10, 10)

6 Plane A and plane B are two distinct planes that are both perpendicular to line ™. Which statement about planes A and B is true?

1) Planes A and B have a common edge, which forms a line.

2) Planes A and B are perpendicular to each other.3) Planes A and B intersect each other at exactly

one point.4) Planes A and B are parallel to each other.

Geometry Regents Exam 0113www.jmap.org

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7 Triangle ABC is similar to triangle DEF. The lengths of the sides of ABC are 5, 8, and 11. What is the length of the shortest side of DEF if its perimeter is 60?1) 102) 12.53) 204) 27.5

8 In the diagram below of right triangle ABC, altitude

CD is drawn to hypotenuse AB.

If AD 3 and DB 12, what is the length of

altitude CD?1) 62) 6 53) 34) 3 5

9 The diagram below shows the construction of an equilateral triangle.

Which statement justifies this construction?1) A B C 1802) mA mB mC3) AB AC BC4) AB BC AC

10 What is the slope of the line perpendicular to the line represented by the equation 2x 4y 12?1) 22) 2

3) 12

4) 12

11 Triangle ABC is shown in the diagram below.

If DE joins the midpoints of ADC and AEB, which statement is not true?

1) DE 12

CB

2) DE Ä CB

3) ADDC

DECB

4) ABC AED

12 The equations x2 y2 25 and y 5 are graphed on a set of axes. What is the solution of this system?1) (0, 0)2) (5, 0)3) (0, 5)4) (5, 5)

13 Square ABCD has vertices A(2,3), B(4,1), C(2, 5), and D(4, 3). What is the length of a side of the square?1) 2 5

2) 2 10

3) 4 5

4) 10 2

Geometry Regents Exam 0113www.jmap.org

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14 The diagram below shows ABD, with ABC

,

BE AD, and EBD CBD.

If mABE 52, what is mD?1) 262) 383) 524) 64

15 As shown in the diagram below, FD and CB

intersect at point A and ET is perpendicular to both

FD and CB at A.

Which statement is not true?

1) ET is perpendicular to plane BAD.

2) ET is perpendicular to plane FAB.

3) ET is perpendicular to plane CAD.

4) ET is perpendicular to plane BAT.

16 Which set of numbers could not represent the lengths of the sides of a right triangle?1) {1, 3, 10 }2) {2, 3, 4}3) {3, 4, 5}4) {8, 15, 17}

17 How many points are 5 units from a line and also equidistant from two points on the line?1) 12) 23) 34) 0

18 The equation of a circle is (x 2)2 (y 5)2 32. What are the coordinates of the center of this circle and the length of its radius?1) (2, 5) and 162) (2,5) and 16

3) (2, 5) and 4 2

4) (2,5) and 4 2

19 The equation of a line is y 23

x 5. What is an

equation of the line that is perpendicular to the given line and that passes through the point (4, 2)?

1) y 23

x 23

2) y 32

x 4

3) y 32

x 7

4) y 32

x 8

20 Consider the relationship between the two statements below.

If 16 9 4 3, then 5 4 3

If 16 9 4 3, then 5 4 3

These statements are1) inverses2) converses3) contrapositives4) biconditionals

Geometry Regents Exam 0113www.jmap.org

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21 In the diagram of trapezoid ABCD below, AB Ä DC ,

AD BC , mA 4x 20, and mC 3x 15.

What is mD?1) 252) 353) 604) 90

22 In circle R shown below, diameter DE is

perpendicular to chord ST at point L.

Which statement is not always true?

1) SL TL2) RS DR

3) RL LE4) (DL)(LE) (SL)(LT)

23 Which equation represents circle A shown in the diagram below?

1) (x 4)2 (y 1)2 3

2) (x 4)2 (y 1)2 3

3) (x 4)2 (y 1)2 9

4) (x 4)2 (y 1)2 9

24 Which equation represents a line that is parallel to the line whose equation is 3x 2y 7?

1) y 32

x 5

2) y 23

x 4

3) y 32

x 5

4) y 23

x 4

25 In the diagram below of circle O, PAC and PBD are secants.

If mCD 70 and mAB 20, what is the degree measure of P?1) 252) 353) 454) 50

Geometry Regents Exam 0113www.jmap.org

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26 The measure of an interior angle of a regular polygon is 120°. How many sides does the polygon have?1) 52) 63) 34) 4

27 As shown in the diagram of rectangle ABCD

below, diagonals AC and BD intersect at E.

If AE x 2 and BD 4x 16, then the length of

AC is1) 62) 103) 124) 24

28 If the vertices of ABC are A(2, 4), B(2, 8), and C(5, 6), then ABC is classified as1) right2) scalene3) isosceles4) equilateral

29 After the transformation r y x, the image of ABC

is AB C . If AB 2x 13 and AB 9x 8, find the value of x.

30 In the diagram below, circles A and B are tangent at

point C and AB is drawn. Sketch all common tangent lines.

31 On the set of axes below, graph the locus of points 4 units from (0, 1) and the locus of points 3 units from the origin. Label with an X any points that satisfy both conditions.

32 Write an equation of a circle whose center is (3, 2) and whose diameter is 10.

Geometry Regents Exam 0113www.jmap.org

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33 Using a compass and straightedge, construct a line perpendicular to line ™ through point P. [Leave all construction marks.]

34 Write an equation of the line that is the perpendicular bisector of the line segment having endpoints (3,1) and (3, 5). [The use of the grid below is optional]

35 A right circular cylinder with a height of 5 cm has a base with a diameter of 6 cm. Find the lateral area of the cylinder to the nearest hundredth of a square centimeter. Find the volume of the cylinder to the nearest hundredth of a cubic centimeter.

36 Triangle ABC has vertices A(5, 1), B(1, 4) and C(1, 1). State and label the coordinates of the vertices of ABC , the image of ABC, following the composite transformation T1,1 û D2.

[The use of the set of axes below is optional.]

37 In ABC, mA x2 12, mB 11x 5, and mC 13x 17. Determine the longest side of

ABC.

Geometry Regents Exam 0113www.jmap.org

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38 The diagram below shows rectangle ABCD with

points E and F on side AB. Segments CE and DF intersect at G, and ADG BCG. Prove:

AE BF

ID: A

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0113geAnswer Section

1 ANS: 1 PTS: 2 REF: 011301ge STA: G.G.29TOP: Triangle Congruency

2 ANS: 2

Parallel chords intercept congruent arcs. 360 (104 168)

2 44

PTS: 2 REF: 011302ge STA: G.G.52 TOP: Chords 3 ANS: 1 PTS: 2 REF: 011303ge STA: G.G.24

TOP: Statements 4 ANS: 3 PTS: 2 REF: 011304ge STA: G.G.56

TOP: Identifying Transformations 5 ANS: 3

6 4 x2

4 x 12

x 8

. 8 2 y

2

2 y 16

y 14

.

PTS: 2 REF: 011305ge STA: G.G.66 TOP: Midpoint 6 ANS: 4 PTS: 2 REF: 011306ge STA: G.G.9

TOP: Planes 7 ANS: 2

Perimeter of DEF is 5 8 11 24. 524

x60

24x 300

x 12.5

PTS: 2 REF: 011307ge STA: G.G.45 TOP: SimilarityKEY: perimeter and area

8 ANS: 1

x2 3 12

x 6

PTS: 2 REF: 011308ge STA: G.G.47 TOP: SimilarityKEY: altitude

9 ANS: 3 PTS: 2 REF: 011309ge STA: G.G.20TOP: Constructions

10 ANS: 2

The slope of 2x 4y 12 is m AB

24

12

. m 2.

PTS: 2 REF: 011310ge STA: G.G.62 TOP: Parallel and Perpendicular Lines 11 ANS: 3 PTS: 2 REF: 011311ge STA: G.G.42

TOP: Midsegments

ID: A

2

12 ANS: 3

x2 52 25

x 0

PTS: 2 REF: 011312ge STA: G.G.70 TOP: Quadratic-Linear Systems 13 ANS: 2

(2 4)2 (3 (1))2 40 4 10 2 10

PTS: 2 REF: 011313ge STA: G.G.39 TOP: Special Parallelograms 14 ANS: 1

180 522

64. 180 (90 64) 26

PTS: 2 REF: 011314ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles 15 ANS: 4 PTS: 2 REF: 011315ge STA: G.G.1

TOP: Planes 16 ANS: 2

22 32 42

PTS: 2 REF: 011316ge STA: G.G.48 TOP: Pythagorean Theorem 17 ANS: 2 PTS: 2 REF: 011317ge STA: G.G.22

TOP: Locus 18 ANS: 4 PTS: 2 REF: 011318ge STA: G.G.73

TOP: Equations of Circles 19 ANS: 4

m 23

m 32

. 2 32

(4) b

2 6 b

8 b

PTS: 2 REF: 011319ge STA: G.G.64 TOP: Parallel and Perpendicular Lines 20 ANS: 1 PTS: 2 REF: 011320ge STA: G.G.26

TOP: Conditional Statements 21 ANS: 3

2(4x 20) 2(3x 15) 360

8x 40 6x 30 360

14x 10 360

14x 350

x 25

. D 3(25) 15 60

PTS: 2 REF: 011321ge STA: G.G.40 TOP: Trapezoids 22 ANS: 3 PTS: 2 REF: 011322ge STA: G.G.49

TOP: Chords 23 ANS: 4 PTS: 2 REF: 011323ge STA: G.G.72

TOP: Equations of Circles

ID: A

3

24 ANS: 3

m AB

32

32

PTS: 2 REF: 011324ge STA: G.G.63 TOP: Parallel and Perpendicular Lines 25 ANS: 1

70 202

25

PTS: 2 REF: 011325ge STA: G.G.51 TOP: Arcs Determined by AnglesKEY: outside circle

26 ANS: 2(n 2)180

n 120

180n 360 120n

60n 360

n 6

.

PTS: 2 REF: 011326ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons 27 ANS: 4

2x 8 x 2

x 10

. AE 10 2 12. AC 2(AE) 2(12) 24

PTS: 2 REF: 011327ge STA: G.G.39 TOP: Special Parallelograms 28 ANS: 3

AB 8 4 4. BC (2 (5))2 (8 6)2 13 . AC (2 (5))2 (4 6)2 13

PTS: 2 REF: 011328ge STA: G.G.69 TOP: Triangles in the Coordinate Plane 29 ANS:

Distance is preserved after the reflection. 2x 13 9x 8

21 7x

3 x

PTS: 2 REF: 011329ge STA: G.G.55 TOP: Properties of Transformations 30 ANS:

PTS: 2 REF: 011330ge STA: G.G.50 TOP: TangentsKEY: common tangency

ID: A

4

31 ANS:

PTS: 2 REF: 011331ge STA: G.G.23 TOP: Locus 32 ANS:

If r 5, then r2 25. (x 3)2 (y 2)2 25

PTS: 2 REF: 011332ge STA: G.G.71 TOP: Equations of Circles 33 ANS:

PTS: 2 REF: 011333ge STA: G.G.19 TOP: Constructions 34 ANS:

M 3 32

, 1 52

Ê

Ë

ÁÁÁÁÁÁˆ

¯

˜̃̃˜̃̃ (3, 2). y 2.

PTS: 2 REF: 011334ge STA: G.G.68 TOP: Perpendicular Bisector 35 ANS:

L 2rh 2 3 5 94.25. V r2h (3)2(5) 141.37

PTS: 4 REF: 011335ge STA: G.G.14 TOP: Volume 36 ANS:

A(11, 1), B(3, 7), C (3, 1)

PTS: 4 REF: 011336ge STA: G.G.58 TOP: Compositions of Transformations

ID: A

5

37 ANS:

x2 12 11x 5 13x 17 180

x2 24x 180 0

(x 30)(x 6) 0

x 6

. mA 62 12 48

mB 11(6) 5 71

mC 13(6) 7 61

. B is the largest angle, so AC in the longest side.

PTS: 4 REF: 011337ge STA: G.G.34 TOP: Angle Side Relationship 38 ANS:

Rectangle ABCD with points E and F on side AB, segments CE and DF intersect at G, and ADG BCE are

given. AD BC because opposite sides of a rectangle are congruent. A and B are right angles and congruent

because all angles of a rectangle are right and congruent. ADF BCE by ASA. AF BE per CPCTC.

EF FE under the Reflexive Property. AF EF BE FE using the Subtraction Property of Segments.

AE BF because of the Definition of Segments.

PTS: 6 REF: 011338ge STA: G.G.27 TOP: Quadrilateral Proofs